Question

Simplify 27 to the negative 2 thirds power. 9 1 over 9 negative 1 over 9 −9

Answer 1

Answer:

The answer is 1/9 ⇒ the second answer

Step-by-step explanation:

* In the exponential functions we have some rules

(1) b^(-m) = 1/(b^m)  (for all nonzero real numbers b)

- If we have negative power we reciprocal the base

 to get positive power

(2) (b^m)^n = b^(mn)

- If we have power over power we multiply them

* In our problem: $(27)^{-\frac{2}{3}}$

- At first change 27 to b^n

∵ 27 = 3 × 3 × 3 = 3³

∴ $27^{-\frac{2}{3}}=(3^{3})^{-\frac{2}{3}}$

* Lets use rule (2)

∴ $27^{-\frac{2}{3}}=3^{-2}$ ⇒ 3 × -2/3 = -2

* Use rule (1)

∴ $3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}$ ⇒ reciprocal the fraction to change the sig of the power

* The answer is 1/9